Criteria for choice between different physical principles

The violation of Bell's inequality is an example of a conflict not between different physical theories, but between different physical principles. The principles which are in conflict are the principles used in the proof of Bell's inequality.

Criteria for the decision between different physical theories have been in the focus of interest of scientific methodology. There is a large set of criteria which can be applied, if the experiment does not (yet) allow to decide the question: First, there is Popper's criterion of empirical content. Then, there are other criteria, like internal consistency, generality, simplicity, explanatory power, and beauty.

The situation is much less clear if we compare physical principles. Physical principles are properties of physical theories, not themself physical theories. Therefore, they do not make themself physical predictions. This is not a rigorous claim – the violation of Bell's inequality is, in some sense, a counterexample, because in this case a particular combination of principles allows to make a nontrivial physical prediction – namely Bell's inequalities – which can be falsified. But this is not really a counterexample, because the falsification of Bell's inequality is based on various physical theories as well, simply these theories are taken to be granted in our considerations.

So, even if we can falsify some combinations of physical principles, it is clearly not the typical property of a physical principle to produce, taken alone, falsifiable predictions. Thus, Popper's criterion of empirical content is inapplicable if we want to decide between physical principles.

Here we propose some metaprinciples or criteria which can be used to decide, in case of conflict, between physical principles:

• The criterion of minimal loss of restrictive power seems to be what can replace Popper's criterion of empirical content. Physical principles restrict the possibilities of theories which are based on these principles. These restrictions following from principles, are able to increase their empirical content. The quite obvious connection between the restrictive power of the principles and the empirical power of the correspondingly restricted theories justifies the criterion. Moreover, it gives this criterion a certain priority: If it allows to make a unique decision, that means, if by omitting or weakening principle A we loose more restrictions than by omitting or weakening principle B, we have to preserve A.
• The criterion of generality simply prefers the more general criterion. This is usually a quite powerful argument, but it cannot be the only one – else, it would never be possible to reject a sufficiently general principle. But, on the other hand, it is a very strong criterion: One needs really good arguments to reject the more general principle.
• The criterion of incompatibility with other principles can be used to justify such a rejection: One conflict of a more general principle is not sufficient to reject it, but if there are several different conflicts with different physical principles, the situation may be different. In this case, the united power of all the rejected principles may be sufficient to overcome the more general principle.
• As well, the criterion of existence of compatible theories for all applications may be used in such a way. For a principle to be viable it is, of course, important that there exist viable theories in all domains of physics which are compatible with this principle. It could be argued that this criterion is the most important one, if not the only important one. There is some truth in this – for a viable physical principle, there should exist some viable physical theory for every application. But we have to take into account the human factor – it may be, as well, that for some application such a theory does not exist not because it is impossible, but simply because nobody has tried yet to develop such a theory. Moreover, theories which are incompatible with the principles preferred by the scientific mainstream are often rejected or simply ignored. Because of this, the criterion of existence of compatible theories favours the mainstream choices in a very strong way.

We apply each of these metaprinciples to our particular conflict between realism and relativity. The result is quite one-sided, giving a strong argument in favour of realism:

• The criterion of minimal loss of restrictive power immediately allows to reject realistic variants of Einstein causality and relativistic symmetry. These variants have to be reduced to their weaker versions, restricted to observables, anyway – if we reject realism or not: If not, because of the conflict with realism. But if we reject realism, these realistic versions become meaningless. The only relativistic principle in conflict with realism which is not covered by this argument is the principle of manifest relativistic symmetry – a strong but highly metaphysical principle.
• The criterion of generality clearly prefers realism – a general principle, applicable and important in all sciences, and not depending on particular assumptions about space and time.
• The criterion of incompatibility with other principles gives us a sufficiently long list of other principles which are incompatible with relativity, starting with absolute time and contemporaneity. It contains the Hamilton formalism, canonical quantization, the Schrödinger equation, local energy and momentum conservation laws including the gravitational field. For realism, this list is empty: The often claimed incompatibility of realism with quantum theory is explicitly proven to be false by a simple counterexample – the pilot wave interpretation.
• Even the criterion of existence of compatible theories does not give support to relativity. Pilot wave versions for quantum field theories have been worked out, and, even if there remain open questions, it seems unreasonable to argue that pilot wave theories will be in principle unable to cover quantum field theory. Instead, standard QFT may be argued to be not manifestly Lorentz invariant – important parts, like the propagators, depend on a choice of a frame, thus, are not manifestly Lorentz-covariant. Only the resulting observable effects are proven to be Lorentz-covariant. But relativistic symmetry for observables only is not in conflict with realism, thus, the compatibility with this weak form of relativistic symmetry is irrelevant for the discussion.
• If we also take into account the theory proposed by the author of these pages (recently published in a peer-reviewed journal, but clearly not yet accepted by the mainstream) we have an example of a realistic theory which has no relativistic competitor: This theory explains the particle content of the standard model. There is, clearly, no relativistic theory which allows to explain the particle content of the standard model. This is the Holy Grail of string theory, but almost hopelessly far away from being reached. And this model quite obviously cannot be put into a four-dimensional spacetime approach: It uses the three dimensions of space to explain the three generations of fermions, the three colors, as well as the three generators of isospin.